r e v b r a s o r t o p . 2 0 1 5;5 0(4):438–444

www.rbo.org .br

Original Article

Study of the metatarsal formula in patient withprimary metatarsalgia�

Eduardo Kenzo Arie, Norma Sueli Albino Moreira, Gilmar Soares Freire,Bruno Schifer dos Santos, Liu Chiao Yi ∗

Santa Casa de Santos, Santos, SP, Brazil

a r t i c l e i n f o

Article history:

Received 24 May 2014

Accepted 17 July 2014

Available online 11 July 2015

Keywords:

Metatarsalgia

Metatarsal bones

Reproducibility of tests

a b s t r a c t

Objectives: The aims of this study were (i) to ascertain the prevalence of different types of

metatarsal formula among patients with primary metatarsalgia; (ii) to compare the variable

of “shortening of the first metatarsal in relation to the second” (I/II) between the metatarsal-

gia and control groups; and (iii) to analyze the intra and interobserver concordance by means

of Morton’s transverse line method and Hardy and Clapham’s arc method.

Methods: A cross-sectional observational study was conducted on 56 patients by means

of radiographs on their 112 ft, of which 56 were in the metatarsalgia group and 56 in the

control group. The evaluations were done between December 2012 and June 2013. The mea-

surements were made by three third-year orthopedics residents with prior training in the

methods used, and a template was used.

Results: There was no concordance between the two methods, as shown by Bland–Altman

plots, although the intraclass correlation coefficients showed that the intra and inter-

observer reproducibility was high using the transverse line method (0.78 and 0.85) and

moderate using the arc method (0.73 and 0.60). Comparison between the groups showed

that there was a statistical difference (p ≤ 0.05) such that there was greater shortening of the

first metatarsal (3.39 mm) in the control group than in the metatarsalgia group (2.14 mm).

In the patients with primary metatarsalgia, the index minus metatarsal formula was more

prevalent according to the transverse line method (62.5%) and the zero plus type according

to the arc method (71.4%).

Conclusion: In the present study, it was observed that the metatarsal formula prevalences

depended on the measurement method. In both groups, shortening of the first metatarsal

predominated. There was no intra or interobserver concordance in either of the two pro-

posed methods.

Brasileira de Ortopedia e Traumatologia. Published by Elsevier Editora

© 2014 Sociedade

Ltda. All rights reserved.

� Work developed in the Orthopedics Service, Santa Casa da Misericórdia de Santos, Santos, SP, Brazil.∗ Corresponding author.

E-mails: liuchiaoyi@yahoo.com.br, liu.unifesp@gmail.com (L.C. Yi).http://dx.doi.org/10.1016/j.rboe.2015.06.0182255-4971/© 2014 Sociedade Brasileira de Ortopedia e Traumatologia. Published by Elsevier Editora Ltda. All rights reserved.

r e v b r a s o r t o p . 2 0 1 5;5 0(4):438–444 439

Estudo da fórmula metatarsal em pacientes com metatarsalgia primária

Palavras-chave:

Metatarsalgia

Ossos do metatarso

Reprodutibilidade dos testes

r e s u m o

Objetivos: Verificar a prevalência dos tipos de fórmula metatarsal (FM) em pacientes com

metatarsalgia primária (MP); comparar a variável “encurtamento do primeiro metatarso

em relacão ao segundo” (I/II) entre os grupos metatarsalgia (GM) e controle (GC); analisar

a concordância intra e interobservadores pelos métodos das linhas transversais (MLT) de

Morton e dos arcos (MA) de Hardy e Clapham.

Métodos: Estudo observacional transversal em 56 pacientes por meio de radiografias dos 112

pés, 56 do GM e 56 do GC avaliados entre dezembro de 2012 e junho de 2013. As mensuracões

foram feitas por três residentes do terceiro ano em ortopedia, com treinamento prévio dos

métodos e uso de template.

Resultados: Não houve concordância em nenhum dos dois métodos verificados pelos gráficos

de Bland–Altman, apesar de o coeficiente de correlacão intraclasses apresentar uma alta

reprodutibilidade intra e interobservadores pelo MLT (0,78 e 0,85) e moderada pelo MA (0,73

e 0,60). Na comparacão entre os grupos, observou-se diferenca estatística (p ≤ 0,05) com um

encurtamento do primeiro metatarso (3,39 mm) maior no GC em relacão ao GM (2,14 mm).

Nos pacientes com MP, a FM tipo index minus foi mais prevalente pelo MLT (62,5%) e o tipo

zero plus pelo MA (71,4%).

Conclusão: Foi observado que a prevalência da FM depende do método de mensuracão. Em

ambos os grupos houve predomínio do encurtamento do primeiro metatarso. Não houve

concordância intra e interobservadores em nenhum dos métodos propostos.

© 2014 Sociedade Brasileira de Ortopedia e Traumatologia. Publicado por Elsevier

Editora Ltda. Todos os direitos reservados.

I

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ntroduction

etatarsalgia, characterized by pain in the plantar regionf the forefoot under the metatarsal heads, is one of theost frequent complaints in clinical practice among con-

itions affecting the feet.1,2 Nearly 80% of the normalopulation present some form of pain in the metatarsalegion over their lifetime.3 The main etiological factorsre biomechanical alterations, which make up 92% of theotal.4 These can be classified as primary, secondary andatrogenic. Primary metatarsalgia alterations are related tohe anatomy of the metatarsals and their relationships,hich can lead to mechanical overload on the affectedetatarsus and may evolve with pain and plantar cal-

osities. In some cases, these consequences may becomencapacitating.1,5

The presence of a short first metatarsus, known as Mor-on’s toe, is considered by many authors to be a contributingactor for the development of primary metatarsalgia.1,3,6

he relationship among the lengths of the metatarsals isefined as the metatarsal formula.3,7 Although this tool

s used both for diagnostic investigation and for guid-nce toward treatment, the choice of the measurementethod and their results are matters of controversy in

he literature. The methods most cited are Morton’s trans-erse line (MTL) and Hardy and Clapham’s arc method

8–10

AM).One crucial aspect in interpreting diagnostic tests is that

he observers’ measurements should be coherent, so that theesults will be reproducible. This is the concept of precision,

which is necessary for the validation of the method and itsusefulness in clinical practice.11

The objectives of the present study were to observe theprevalence of the types of metatarsal formula among patientswith primary metatarsalgia; compare the variable of “shorten-ing of the first metatarsus in relation to the second” betweenthe metatarsalgia group (MG) and the control group (CG); andanalyze the intra and inter-observer agreement through theMTL and AM methods.

Methods

This was a cross-sectional observational study on 56 patients(112 ft), over the age of 18 years and all female, who weredivided into 28 patients (56 ft) in the MG and 28 (56 ft) in theCG.

The MG consisted of patients with painful symptoms in theregion of the metatarsal heads, who had been diagnosed aspresenting primary metatarsalgia due to mechanical overload.The CG was composed of patients with plantar fasciitis, whopresented pain in the hindfoot region.

Patients were excluded if they presented deformities thatcompromised the forefoot, midfoot or hindfoot; a personalhistory of previous surgery or trauma to the feet; or personalhistories of diabetes mellitus, rheumatological diseases, vas-cular diseases or neuropathies.

This study was approved by the research ethics commit-tee (Platform Brazil procedural no. 152078 of November 30,2012) and all participants signed a free and informed consentstatement.

p . 2 0 1 5;5 0(4):438–444

Table 1 – Relative difference in length between the firstand second metatarsals.

Observer Method Mean (SD)

A Transverse lines −2.77 mm (2.90)Arc 0.04 mm (2.90)

B Transverse lines −2.72 mm (2.87)Arc 0.42 mm (2.88)

C Transverse lines −2.47 mm (3.04)Arc −0.88 mm (2.94)

mm, millimeters; SD, standard deviation.

Table 2 – Comparison of the interobserver agreementanalysis between the transverse line method and the arcmethod.

Method ICC CI p

Transverse lines 0.85 [0.81; 0.89] 0.104Arc 0.60 [0.50; 0.69] 0.001a

ICC, intraclass correlation coefficient; CI, confidence interval; p, sig-nificance level of the analysis of variance in blocks.

the observers, using either the MTL or the AM.

Table 3 – Statistical analysis on the comparisonsbetween observers, two by two.

Observers compared p

C–A 0.001a

C–B 0.002a

440 r e v b r a s o r t o

Procedures

Three medical residents in orthopedics who were in their thirdyear of specialization and under the supervision of the princi-pal investigator evaluated all the patients with complaints ofpain in their feet who went through the outpatient service ofour department between December 2012 and June 2013.

The volunteers underwent simple radiography on both feetin the upright standing position, in true dorsoplantar viewwith a cranial angle of 15◦, at real size.12

Reproducibility

To assess interobserver reliability, all the radiographic imageswere measured using the MTL and AM separately by threeobservers.

To assess intraobserver reliability, one of the observers wasrandomly chosen to perform the measurements again, eightweeks after the first evaluation.

All three observers received prior training on the mea-surement methods. To help the evaluation and make it morereliable and reproducible, an illustrative and explanatorymodel for both methods was attached beside the registrationform (Fig. 1).

Morton’s transverse line method of measurement wasapplied schematically: 1 – set up a line over the diaphyseal axisof the second metatarsal; 2 – draw a transverse line perpen-dicular to the apex of the head of the first metatarsal; 3 – drawa transverse line perpendicular to the apex of the head of thesecond metatarsal; 4 – measure the distance between thesetwo transverse lines in millimeters. Hardy and Clapham’s arcmethod was also applied schematically: 1 – set up a line overthe diaphyseal axis of the second metatarsal; 2 – mark thecenter of the arcs at the intersection of this line with anotherline that touches the most medial point of talonavicular andthe most lateral point of calcaneocuboid; 3 – draw an arcthat touches the apex of the head of the first metatarsal; 4– draw an arc that touches the apex of the head of the secondmetatarsal; 5 – measure the distance between these two arcsin millimeters.6–9

Statistical analysis

Based on a pilot study performed previously and consider-ing the variable of “relative difference in the length betweenthe first and second metatarsals” (I/II), the sample size wasdefined as 28 patients per group, with a power of 80% andsignificance level of 0.05.

The descriptive analysis was presented as the mean andstandard deviation of the variables analyzed. To evaluate intraand interobserver reliability, the interclass correlation coeffi-cient (ICC) was applied and classified as: minimal (≤0.25), low(between 0.26 and 0.49), moderate (between 0.50 and 0.69),high (between 0.70 and 0.89) or very high (≥0.90).13

Single-factor analysis of variance was used to compare the

CG and the MG regarding the variable I/II.

To observe the prevalences of the types of metatarsalformula, Viladot’s classification3,14 as modified by Mancusoet al.15 was used, considering two types: values lower than

a p ≤ 0.05.

−0.5 mm were classified as index minus and positive valuesas zero plus.

Results

The descriptive data and the statistical analysis results wereas follows:

Table 1 shows the mean and standard deviation (SD) of themeasurements on the variable I/II using both the MTL and theAM by all three observers.

Table 2 demonstrates that the MTL presented higher ICCand lower CI, in comparison with the AM, while in analysisof variance divided into blocks, the AM presented a signifi-cant difference (p ≤ 0.05), which demonstrated disagreementbetween the observers.

The Bonferroni method shown in Table 3 demonstratedthat the means of observers A and B differed (p ≤ 0.05) fromthe mean of observer C, using the AM.

Figs. 2 and 3 present the results from the Bland–Altmanplots, which indicated that there was no agreement among

B–A 0.296

p, significance level.a p ≤ 0.05.

r e v b r a s o r t o p . 2 0 1 5;5 0(4):438–444 441

Fig. 1 – Previous training and template for measurements using Morton’s transverse line method (A) and Hardy andClapham’s arc method (B).

3

2

1

0

–2–4–6–8 0Means of the evaluations

Sta

ndar

d de

viat

ions

of t

he e

valu

atio

ns

2

usi

at

Fig. 2 – Interobserver evaluation

Table 4 presents the descriptive measurements on the vari-ble I/II, according to the MTL and AM, made by observer A atwo different times.

Table 4 – Relative difference in length between the firstand second metatarsals.

Evaluations Method Mean (SD)

1sttime

Transverse lines −2.77 mm (2.90)Arc 0.04 mm (2.90)

2ndtime

Transverse lines −2.57 mm (2.80)Arc 0.06 mm (2.77)

SD, standard deviation; mm, millimeters.

ng the transverse line method.

Table 5 demonstrates that the MTL obtained a higher ICC

and lower CI than the AM did. The Student t test indicated thatthere was agreement between the evaluations using the twomethods.

Table 5 – Comparison analysis on intraobserveragreement.

Method ICC CI p

Transverse lines 0.78 [0.70; 0.84] 0.275Arc 0.73 [0.64; 0.81] 0.909

ICC, intraclass correlation coefficient; CI, confidence interval; p, sig-nificance level of the Student t test analysis.a p ≤ 0.05.

442 r e v b r a s o r t o p . 2 0 1 5;5 0(4):438–444

6

Sta

ndar

d de

viat

ions

of t

he e

valu

atio

ns

–2–4 420Means of the evaluations

6

4

2

0

luati

Fig. 3 – Interobserver eva

Figs. 4 and 5 indicate that there was no agreement betweenthe evaluations using either the MTL or the AM.

Comparisons between the groups were made using the first

measurements from observer A, by means of the MTL.

The mean value of the descriptive measurements on thevariable I/II in the MG was −2.14 mm (SD = 3.05) and in the CGit was −3.39 mm (SD = 2.63) (Fig. 6).

–4–6–8Mean (Evaluation

–6

–4

–2

0

2

4

Eva

luat

ion

1 –

Eva

luat

ion

2

Fig. 4 – Intraobserver evaluation usi

–6Mean (Evaluation

–2–4 0

–10

–5

0

Eva

luat

ion

1 –

Eva

luat

ion

2

5

Fig. 5 – Intraobserver evaluati

on using the arc method.

The result from inferential analysis to compare the CG andthe MG regarding the variable I/II was used in a single-factormixed model of variance. This indicated that there was a dif-

ference (p ≤ 0.05) between the means of the CG and MG.

Table 6 shows a descriptive comparison between the MTLand AM regarding the prevalences of types of metatarsal for-mula in the CG and MG. The MG showed higher prevalence of

–2 0 2 1, Evaluation 2)

Mean –2 SD

Mean

Mean +2 SD

ng the transverse line method.

1, Evaluation 2)

Mean –2 SD

Mean

Mean +2 SD

2 4 6

on using the arc method.

r e v b r a s o r t o p . 2 0 1 5

Control Metatarsalgia

–8

–6

–4

0

2

4

Rel

ativ

e di

ffere

nce

–2

Fig. 6 – Distribution of the variable of “relative difference ofthe length between the first and second metatarsal”,according to each group.

Table 6 – Prevalence of the types of metatarsal formulain the general sample and in the groups.

Method Metatarsalformula

Metatarsalgiagroup

Controlgroup

Transverselines

Index minus 62.5% 85.7%Zero plus 37.5% 14.3%

fafCma

D

Tmcmwt

mmmotTHgfnnow

between two methods, the agreement between the evalu-

Arc Index minus 28.6% 53.6%Zero plus 71.4% 46.4%

eet with the index minus type of metatarsal formula (62.50%)ccording to the MTL, while the zero plus type of metatarsalormula was more prevalent according to the AM (71.43%). TheG presented higher prevalence of the index minus type ofetatarsal formula (85.71%) according to the MTL, and also

ccording to the AM (53.57%).

iscussion

he length relationships between the metatarsals, more com-only known as the metatarsal formula, is a matter of

ontroversy in the literature with regard to both the choice ofethod for measurement and the association of this conditionith the development of several disorders that compromise

he forefoot, such as primary metatarsalgia.7,10

The results from the present study showed that measure-ent of the metatarsal formula through the transverse lineethod is related to higher prevalence of feet with a secondetatarsal longer than the first (index minus). The same was

bserved by Morton,6 who correlated this type of foot as a con-ributing factor for the development of primary metatarsalgia.his concept has been established by several authors.1,3,5

owever, when the same method was used for the controlroup, even greater prevalence of the index minus type ofoot was observed, as also seen by Barroco et al.12 among 332ormal feet in their study. In comparing the means of the

umerical variable of “relative difference between the lengthf the first and second metatarsals”, a significant differenceas observed (p ≤ 0.05). However, this finding was the inverse

;5 0(4):438–444 443

of the conceptual hypothesis, with greater shortening of thefirst metatarsal in the control group than in the metatarsalgiagroup. This result, combined with data in the literature,12 con-tradicts the “Morton’s toe” theory and demonstrates that feetwith shortening of the first metatarsal or with an index minustype of metatarsal formula measured through the transverseline method are in fact the most prevalent type of feet amongthe general population.

The present study found that the prevalences of differ-ent types of metatarsal formula among patients with primarymetatarsalgia depend on the measurement method. Unlikein the transverse line method, the most prevalent type ofmetatarsal formula observed through the arc method is thezero plus formula, as observed by Hardy and Clapham andother authors.9,16,17 This phenomenon possibly occurs dueto technical differences between the measurements: whenpatients with a high intermetatarsal angle (greater than 9◦)are evaluated, there is a relative decrease in the length of thefirst metatarsal as measured through Morton’s transverse linemethod. However, when patients whose feet do not presentdeformities are evaluated, as was the case in the present study,in which the patients presented a normal intermetatarsalangle (between 0◦ and 8◦), there is a relative increase in thelength of the first metatarsal when measured through Hardyand Clapham’s arc method.15

Several ways to measure metatarsal length have beendescribed in the literature, such as anatomopathologicalassessments on the feet of cadavers,18 clinical parameters,19

lateral-view radiography,20 tomography21 and computer-based measurement,22 even for surgical planning.23 However,the manual radiographic method of measuring the relativelength of Morton’s transverse lines and Hardy and Clapham’sarcs are the methods most cited and used as diagnosticinstruments.7,9,10

In the present study, the evaluations made by the third-year orthopedic residents, who had received previous trainingand used a template, did not present intra and interobserveragreement using either method. The transverse line methodpresented a greater correlation coefficient than that of thearc method, possibly due to the simplicity of the technique,since the arc method has one additional step. This step com-prises an additional line that is drawn on the Chopart joint,and this was considered by the observers to be the disagree-ment factor. However, in another study, none of the methodspresented agreement according to the Bland and Altmanmethod.24 When the mean values from the intra and interob-server evaluations were paired and plotted with their standarddeviations and agreement limits, instead of finding resultsnear the zero line of equality, the results were very discrepant.This demonstrates the lack of agreement and reproducibilityof the methods and, thus, puts their use in clinical practiceinto question.

The reproducibility of a test indicates the precision ofthe method and determines its validity and use in clin-ical practice.11 The Bland and Altman statistical methodis the methodology most used to analyze the agreement

ations of two or more observers using the same method,or even the agreement between the evaluations of thesame observer at different times, for the same method. Use

p . 2 0

r

1

1

1

1

1

1

1

1

1

1

2

2

2

2

2

2

26. Zaki R, Bulgiba A, Ismail NA. Statistical methods used to testfor agreement of medical instruments measuring continuous

444 r e v b r a s o r t o

of the correlation coefficients in isolation is inappropriatebecause this may bring incomplete information and inade-quate interpretations.25,26

A diagnostic technique should present precision and repro-ducibility, with consistency over different observations andlittle variability. However, the techniques proposed to assessthe metatarsal formula cannot be compared or standardized,precisely because the current subjective criteria present greatintra and interobserver variability.

Different methods for measuring the length of themetatarsals have the potential to give rise to different results,with potential consequences for surgical planning. In the lightof the current results, surgical treatment based only on thisradiographic parameter is, to say the least, questionable. Clin-ical examination must be the priority in recommending anymetatarsal osteotomy and should be complemented by otherparameters, such as assessment of the instability of the firstray and anatomical alterations of the metatarsals in the coro-nal plane.

Conclusion

It was observed that the prevalence of the metatarsal formuladepends on the measurement method. In cases of primarymetatarsalgia, the index minus type is related to Morton’smethod, while the zero plus type is related to Hardy andClapham’s method.

In comparing the CG and the MG using Morton’s transverseline method, there was predominance of shortening of the firstmetatarsal in both groups.

The methods for measuring the metatarsal formulaapplied in the present study did not show any intra or inter-observer agreement.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgement

We are grateful to Dr. Mauricio Sgarbi for enabling and sup-porting this study.

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